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Daisuke Sagaki - One of the best experts on this subject based on the ideXlab platform.
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a uniform Model for kirillov reshetikhin crystals ii alcove Model Path Model and p x
International Mathematics Research Notices, 2016Co-Authors: Cristian Lenart, Satoshi Naito, Daisuke Sagaki, Anne Schilling, Mark ShimozonoAbstract:Author(s): Lenart, Cristian; Naito, Satoshi; Sagaki, Daisuke; Schilling, Anne; Shimozono, Mark | Abstract: We establish the equality of the specialization $P_\lambda(x;q,0)$ of the Macdonald polynomial at $t=0$ with the graded character $X_\lambda(x;q)$ of a tensor product of "single-column" Kirillov-Reshetikhin (KR) modules for untwisted affine Lie algebras. This is achieved by constructing two uniform combinatorial Models for the crystals associated with the mentioned tensor products: the quantum alcove Model (which is naturally associated to Macdonald polynomials), and the quantum Lakshmibai-Seshadri Path Model. We provide an explicit affine crystal isomorphism between the two Models, and realize the energy function in both Models. In particular, this gives the first proof of the positivity of the $t = 0$ limit of the symmetric Macdonald polynomial in the untwisted and non-simply-laced cases, when it is expressed as a linear combination of the irreducible characters for a finite-dimensional simple Lie subalgebra, as well as a representation-theoretic meaning of the coefficients in this expression in terms of degree functions.
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semi infinite lakshmibai seshadri Path Model for level zero extremal weight modules over quantum affine algebras
Advances in Mathematics, 2016Co-Authors: Motohiro Ishii, Satoshi Naito, Daisuke SagakiAbstract:Abstract We introduce semi-infinite Lakshmibai–Seshadri Paths by using the semi-infinite Bruhat order (or equivalently, Lusztig's generic Bruhat order) on affine Weyl groups in place of the usual Bruhat order. These Paths enable us to give an explicit realization of the crystal basis of an extremal weight module of an arbitrary level-zero dominant integral extremal weight over a quantum affine algebra. This result can be thought of as a full generalization of the previous result due to Naito and Sagaki (which uses Littelmann's Lakshmibai–Seshadri Paths), in which the level-zero dominant integral weight is assumed to be a positive-integer multiple of a level-zero fundamental weight.
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semi infinite lakshmibai seshadri Path Model for level zero extremal weight modules over quantum affine algebras
arXiv: Quantum Algebra, 2014Co-Authors: Motohiro Ishii, Satoshi Naito, Daisuke SagakiAbstract:We introduce semi-infinite Lakshmibai-Seshadri Paths by using the semi-infinite Bruhat order (or equivalently, Lusztig's generic Bruhat order) on affine Weyl groups in place of the usual Bruhat order. These Paths enable us to give an explicit realization of the crystal basis of an extremal weight module of an arbitrary level-zero dominant integral extremal weight over a quantum affine algebra. This result can be thought of as a full generalization of our previous result (which uses Littelmann's Lakshmibai-Seshadri Paths), in which the level-zero dominant integral weight is assumed to be a positive-integer multiple of a level-zero fundamental weight.
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a uniform Model for kirillov reshetikhin crystals ii alcove Model Path Model and p x
arXiv: Quantum Algebra, 2014Co-Authors: Cristian Lenart, Satoshi Naito, Daisuke Sagaki, Anne Schilling, Mark ShimozonoAbstract:We establish the equality of the specialization $P_\lambda(x;q,0)$ of the Macdonald polynomial at $t=0$ with the graded character $X_\lambda(x;q)$ of a tensor product of "single-column" Kirillov-Reshetikhin (KR) modules for untwisted affine Lie algebras. This is achieved by constructing two uniform combinatorial Models for the crystals associated with the mentioned tensor products: the quantum alcove Model (which is naturally associated to Macdonald polynomials), and the quantum Lakshmibai-Seshadri Path Model. We provide an explicit affine crystal isomorphism between the two Models, and realize the energy function in both Models. In particular, this gives the first proof of the positivity of the $t = 0$ limit of the symmetric Macdonald polynomial in the untwisted and non-simply-laced cases, when it is expressed as a linear combination of the irreducible characters for a finite-dimensional simple Lie subalgebra, as well as a representation-theoretic meaning of the coefficients in this expression in terms of degree functions.
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Path Model for a level zero extremal weight module over a quantum affine algebra ii
Advances in Mathematics, 2006Co-Authors: Satoshi Naito, Daisuke SagakiAbstract:Abstract Let ϖ i be a level-zero fundamental weight for an affine Lie algebra g over Q , and let B ( ϖ i ) be the crystal of all Lakshmibai–Seshadri Paths of shape ϖ i . First, we prove that the crystal graph of B ( ϖ i ) is connected. By combining this fact with the main result of our previous work, we see that B ( ϖ i ) is, as a crystal, isomorphic to the crystal base B ( ϖ i ) of the extremal weight module V ( ϖ i ) over a quantum affine algebra U q ( g ) over Q (q) of extremal weight ϖ i . Next, we obtain an explicit description of the decomposition of the crystal B ( m ϖ i ) of all Lakshmibai–Seshadri Paths of shape m ϖ i into connected components. Furthermore, we prove that B ( m ϖ i ) is, as a crystal, isomorphic to the crystal base B ( m ϖ i ) of the extremal weight module V ( m ϖ i ) over U q ( g ) of extremal weight m ϖ i .
Satoshi Naito - One of the best experts on this subject based on the ideXlab platform.
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a uniform Model for kirillov reshetikhin crystals ii alcove Model Path Model and p x
International Mathematics Research Notices, 2016Co-Authors: Cristian Lenart, Satoshi Naito, Daisuke Sagaki, Anne Schilling, Mark ShimozonoAbstract:Author(s): Lenart, Cristian; Naito, Satoshi; Sagaki, Daisuke; Schilling, Anne; Shimozono, Mark | Abstract: We establish the equality of the specialization $P_\lambda(x;q,0)$ of the Macdonald polynomial at $t=0$ with the graded character $X_\lambda(x;q)$ of a tensor product of "single-column" Kirillov-Reshetikhin (KR) modules for untwisted affine Lie algebras. This is achieved by constructing two uniform combinatorial Models for the crystals associated with the mentioned tensor products: the quantum alcove Model (which is naturally associated to Macdonald polynomials), and the quantum Lakshmibai-Seshadri Path Model. We provide an explicit affine crystal isomorphism between the two Models, and realize the energy function in both Models. In particular, this gives the first proof of the positivity of the $t = 0$ limit of the symmetric Macdonald polynomial in the untwisted and non-simply-laced cases, when it is expressed as a linear combination of the irreducible characters for a finite-dimensional simple Lie subalgebra, as well as a representation-theoretic meaning of the coefficients in this expression in terms of degree functions.
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semi infinite lakshmibai seshadri Path Model for level zero extremal weight modules over quantum affine algebras
Advances in Mathematics, 2016Co-Authors: Motohiro Ishii, Satoshi Naito, Daisuke SagakiAbstract:Abstract We introduce semi-infinite Lakshmibai–Seshadri Paths by using the semi-infinite Bruhat order (or equivalently, Lusztig's generic Bruhat order) on affine Weyl groups in place of the usual Bruhat order. These Paths enable us to give an explicit realization of the crystal basis of an extremal weight module of an arbitrary level-zero dominant integral extremal weight over a quantum affine algebra. This result can be thought of as a full generalization of the previous result due to Naito and Sagaki (which uses Littelmann's Lakshmibai–Seshadri Paths), in which the level-zero dominant integral weight is assumed to be a positive-integer multiple of a level-zero fundamental weight.
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semi infinite lakshmibai seshadri Path Model for level zero extremal weight modules over quantum affine algebras
arXiv: Quantum Algebra, 2014Co-Authors: Motohiro Ishii, Satoshi Naito, Daisuke SagakiAbstract:We introduce semi-infinite Lakshmibai-Seshadri Paths by using the semi-infinite Bruhat order (or equivalently, Lusztig's generic Bruhat order) on affine Weyl groups in place of the usual Bruhat order. These Paths enable us to give an explicit realization of the crystal basis of an extremal weight module of an arbitrary level-zero dominant integral extremal weight over a quantum affine algebra. This result can be thought of as a full generalization of our previous result (which uses Littelmann's Lakshmibai-Seshadri Paths), in which the level-zero dominant integral weight is assumed to be a positive-integer multiple of a level-zero fundamental weight.
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a uniform Model for kirillov reshetikhin crystals ii alcove Model Path Model and p x
arXiv: Quantum Algebra, 2014Co-Authors: Cristian Lenart, Satoshi Naito, Daisuke Sagaki, Anne Schilling, Mark ShimozonoAbstract:We establish the equality of the specialization $P_\lambda(x;q,0)$ of the Macdonald polynomial at $t=0$ with the graded character $X_\lambda(x;q)$ of a tensor product of "single-column" Kirillov-Reshetikhin (KR) modules for untwisted affine Lie algebras. This is achieved by constructing two uniform combinatorial Models for the crystals associated with the mentioned tensor products: the quantum alcove Model (which is naturally associated to Macdonald polynomials), and the quantum Lakshmibai-Seshadri Path Model. We provide an explicit affine crystal isomorphism between the two Models, and realize the energy function in both Models. In particular, this gives the first proof of the positivity of the $t = 0$ limit of the symmetric Macdonald polynomial in the untwisted and non-simply-laced cases, when it is expressed as a linear combination of the irreducible characters for a finite-dimensional simple Lie subalgebra, as well as a representation-theoretic meaning of the coefficients in this expression in terms of degree functions.
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Path Model for a level zero extremal weight module over a quantum affine algebra ii
Advances in Mathematics, 2006Co-Authors: Satoshi Naito, Daisuke SagakiAbstract:Abstract Let ϖ i be a level-zero fundamental weight for an affine Lie algebra g over Q , and let B ( ϖ i ) be the crystal of all Lakshmibai–Seshadri Paths of shape ϖ i . First, we prove that the crystal graph of B ( ϖ i ) is connected. By combining this fact with the main result of our previous work, we see that B ( ϖ i ) is, as a crystal, isomorphic to the crystal base B ( ϖ i ) of the extremal weight module V ( ϖ i ) over a quantum affine algebra U q ( g ) over Q (q) of extremal weight ϖ i . Next, we obtain an explicit description of the decomposition of the crystal B ( m ϖ i ) of all Lakshmibai–Seshadri Paths of shape m ϖ i into connected components. Furthermore, we prove that B ( m ϖ i ) is, as a crystal, isomorphic to the crystal base B ( m ϖ i ) of the extremal weight module V ( m ϖ i ) over U q ( g ) of extremal weight m ϖ i .
James D. Meindl - One of the best experts on this subject based on the ideXlab platform.
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a stochastic wire length distribution for gigascale integration gsi ii applications to clock frequency power dissipation and chip size estimation
IEEE Transactions on Electron Devices, 1998Co-Authors: Jeffrey A. Davis, Vivek De, James D. MeindlAbstract:For pt.I see ibid., vol.45, no.3, pp.580-9 (Mar. 1998). Based on Rent's Rule, a well-established empirical relationship, a complete wire-length distribution for on-chip random logic networks is used to enhance a critical Path Model; to derive a preliminary dynamic power dissipation Model; and to describe optimal architectures for multilevel wiring networks that provide maximum interconnect density and minimum chip size.
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A stochastic wire length distribution for gigascale integration (GSI)
Proceedings of CICC 97 - Custom Integrated Circuits Conference, 2024Co-Authors: Jeffrey A. Davis, James D. MeindlAbstract:Based on Rent's Rule, a well established empirical relationship, a rigorous derivation of a complete wire length distribution for on-chip random logic networks is performed. This distribution is used to enhance a critical Path Model; to derive a preliminary dynamic power dissipation Model; and to describe optimal architectures for multilevel wiring networks that provide maximum interconnect density.
Motohiro Ishii - One of the best experts on this subject based on the ideXlab platform.
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semi infinite lakshmibai seshadri Path Model for level zero extremal weight modules over quantum affine algebras
Advances in Mathematics, 2016Co-Authors: Motohiro Ishii, Satoshi Naito, Daisuke SagakiAbstract:Abstract We introduce semi-infinite Lakshmibai–Seshadri Paths by using the semi-infinite Bruhat order (or equivalently, Lusztig's generic Bruhat order) on affine Weyl groups in place of the usual Bruhat order. These Paths enable us to give an explicit realization of the crystal basis of an extremal weight module of an arbitrary level-zero dominant integral extremal weight over a quantum affine algebra. This result can be thought of as a full generalization of the previous result due to Naito and Sagaki (which uses Littelmann's Lakshmibai–Seshadri Paths), in which the level-zero dominant integral weight is assumed to be a positive-integer multiple of a level-zero fundamental weight.
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semi infinite lakshmibai seshadri Path Model for level zero extremal weight modules over quantum affine algebras
arXiv: Quantum Algebra, 2014Co-Authors: Motohiro Ishii, Satoshi Naito, Daisuke SagakiAbstract:We introduce semi-infinite Lakshmibai-Seshadri Paths by using the semi-infinite Bruhat order (or equivalently, Lusztig's generic Bruhat order) on affine Weyl groups in place of the usual Bruhat order. These Paths enable us to give an explicit realization of the crystal basis of an extremal weight module of an arbitrary level-zero dominant integral extremal weight over a quantum affine algebra. This result can be thought of as a full generalization of our previous result (which uses Littelmann's Lakshmibai-Seshadri Paths), in which the level-zero dominant integral weight is assumed to be a positive-integer multiple of a level-zero fundamental weight.
Yanjun Guan - One of the best experts on this subject based on the ideXlab platform.
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career construction in social exchange a dual Path Model linking career adaptability to turnover intention
Journal of Vocational Behavior, 2019Co-Authors: Fei Zhu, Zijun Cai, Emma Ellen Kathrina Buchtel, Yanjun GuanAbstract:Abstract Although the negative relationship between career adaptability and turnover intention has been established in previous research, understanding of the mechanisms and boundary conditions is still incomplete. In this study we attempt to address this gap by developing a dual-Path moderated mediation Model based on career construction theory, social exchange theory and trait activation theory. Specifically, we propose two mediators - career satisfaction and perceived organizational support (POS) - to explain the negative effect of career adaptability on turnover intention. Moreover, following the trait activation perspective, we propose that organizational brands, including symbolic and instrumental brands, could separately moderate these two mediation Paths. We collected multi-source data among a sample of 1013 employees and 200 HRs from 200 organizations in China to test these ideas. The results show that both career satisfaction and POS mediate the negative effect of career adaptability on turnover intention. Moreover, the mediation Path through career satisfaction to turnover intention is stronger in companies with more favorable symbolic brands, and the mediation Path through POS to turnover intention is stronger in companies with more favorable instrumental brands. The findings have important implications for both career construction research and organizational career management practices.
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career adaptability and perceived overqualification testing a dual Path Model among chinese human resource management professionals
Journal of Vocational Behavior, 2015Co-Authors: Weiguo Yang, Yanjun Guan, Xin Lai, Zhuolin She, Andrew LockwoodAbstract:Based on career construction theory, the current research examined the relationship between career adaptability and perceived overqualification among a sample of Chinese human resource management professionals (N = 220). The results of a survey study showed that career adaptability predicted perceived overqualification through a dual-Path Model: On the one hand, career adaptability positively predicted employees' perceived delegation, which had a subsequent negative effect on perceived overqualification. At the same time, career adaptability also positively predicted career anchor in challenge, which in turn positively predicted overqualification. This dual-Path mediation Model provides a novel perspective to understand the mechanisms through which career adaptability affects perceived overqualification, and demonstrates the coexistence of opposite effects in this process. In addition, the results also showed that the effects of perceived delegation and career anchor in challenge on perceived overqualification were stronger among employees with a higher (vs. lower) level of organizational tenure. These findings carry implications for both career development theories and organizational management practices.
